reproducing an e 6 ssm from its signatures

04/19/23 Steve King, LHC Inverse Workshop, MCTP

Reproducing an EReproducing an E66SSM from its SSM from its SignaturesSignatures

•LHC-IA - What is the new physics?

•LHC-IB - What is the spectrum and effective Lagrangian of the new physics at the weak scale?

•LHC-IC - How can we begin to study what the underlying theory is, perhaps at a high scale and/or in extra dimensions?

The LHC Inverse Problem:The LHC Inverse Problem: Nima Arkani-HamedGordy Kane

In this talk we discuss the LHC Inverse problem from the perspective of an E6 Supersymmetric Standard Model (shortly defined)


•Although MSSM solves “technical hierarchy problem” (loops) it does not address “tree-level hierarchy problem” of why Higgs masses are low

•In particular no reason why parameter (which respects SUSY) should be same order as soft masses the “ problem”.

•In M-theory this cannot be resolved a la Guidice-Masiero using the Kahler term HuHd if Hu and Hd come from 27’s of E6 since 27£ 27 is not invariant

•In the NMSSM =0 but an effective -term is generated from a singlet: S Hu Hd ! <S> Hu Hd where singlet VEV <S> plays role of parameter

•A coupling S3 is required to avoid a massless axion due to global U(1) PQ symmetry which broken at weak scale.

•With S3 term the symmetry is reduced to Z3 -- broken at the weak scale resulting in cosmological domain walls (or tadpoles if broken)

The The problemproblem


•We would like to solve problem of MSSM using a singlet as in the NMSSM, but avoiding the domain wall/ tadpole problems of NMSSM

•The idea is to use the superpotential coupling W= S Hu Hd (without the extra S3 term) and gauge the U(1) PQ symmetry so that the dangerous axion is eaten to form a massive Z’ gauge boson U(1)’ model

•Anomaly cancellation in low energy gauged U(1)’ models always implies either extra low energy exotic matter or family-nonuniversal U(1)’ charges

•The E6SSM is an example of a U(1)’ model with extra low energy exotic matter with anomalies are cancelled elegantly using complete 27’s of E6

The EThe E66SSM SSM solutionsolution


Other related references Other related references (very incomplete – apologies)(very incomplete – apologies)

Cvetic, Demir, Espinosa, Everett, Langacker; J.Wang;

Keith, Ma;

Daikoku, Suematsu;

Demir, Everett;

Hewett, Rizzo;

Demir, Kane, T.Wang;

Morrissey, Wells;

Barger, Langacker, Lee, Shaughnessy;

EE66SSM is discussed in SSM is discussed in SFK, Moretti and Nevzorov


Sketch of the ESketch of the E66SSM SSM

15 14 4(1) (1) (1) NU U U

(10) (5) (1)SO SU U 6 (10) (1)E SO U

E6 ! SU(5)£U(1)N MGUT

TeV U(1)N broken, Z’ and exotics get mass, term generated

27',27'

Incomplete multiplets

(required for unification)

Right handed neutrino masses

MString E8 £ E8 ! E

6

Quarks, leptons

Exotics and Higgs

Singlets and RH s

H’,H’-bar

MW SU(2)L£ U(1)Y broken

Right handed neutrinos are neutral under:


Exotic D,D-bar

Higgs and non-Higgs Non-Higgs from incomplete reps 27’+27’-bar

Singlets Right-handed neutrinos

Quarks and Leptons

27i

Low energy matter content of ELow energy matter content of E66SSMSSM


Family Universal Anomaly Free Charges:

Most general E6 allowed couplings from 273:

Rapid proton decay! Need generalization of R-parity two possibilities:

I. Z2L under which leptons are odd forbids W2 exotic D,D-bar are diquarks

II. Z2B with leptons & D,D-bar odd forbids W1 exotic D,D-bar are leptoquarks


Including RH neutrino masses have two models:

To suppress FCNCs we further assume an approximate Z2H symmetry under which

only Hd = H1,3, Hu=H2,3 S=S3 are even (all else=odd)

Suppresses W1, W2 and restricts W0 as follows (e.g. only one pair of Higgs doublets couple to quarks and leptons as in the MSSM and will get radiative VEVs):

In phenomenological studies we keep only terms with large Yukawa couplings:

However terms with small Yukawa couplings arising from W1 or W2. are required for exotic decays.


The origin of bilinear The origin of bilinear massesmassesRight-handed neutrino masses arise from the coupling to

the Higgs 27H which breaks E6

•We also need to generate a TeV mass term H’ H’-bar

•The simplest possibility is to use the Guidice-Masiero mechanism

•The Kahler potential permits H’ H’-bar since H’ comes from 27’ and H’-bar comes from 27’-bar

•Unlike Hu Hd which is forbidden since 27£ 27 is not invariant

•Note that H’,H’-bar are irrelevant for Higgs phenomenology since they do not develop VEVs – they are ``non-Higgs’’


Higgs Phenomenology of EHiggs Phenomenology of E66SSM @ LHCSSM @ LHCWith Z2

H only three Higgs multiplets Hu, Hd, S get VEVs

W= S Hd Hd as in the NMSSM but without the S3 term (simpler!)

This leads to the Higgs potential:

Extra scalar state compared to MSSM – as in the NMSSM.

As in the MSSM (unlike the NMSSM since the axion is eaten by the Z’)

As in the MSSM and NMSSM

Can the Higgs sector of the E6SSM be distinguished from that of the MSSM and NMSSM?

1h2h

3h

3h

1h

3, ,H A h

Small < g1 gives an MSSM-like spectrum @ LHC (unfortunately!) Satisfies the MSSM bound

1h

2h

3h

3h

2h1h

2h

singlet

3, ,H A h

3h

3h

2h

1h

1hLarge > g1 leads to only h1 @ LHC

1h

2h

3h

3h

2h1h

Too heavy to be observed @LHC

mainly singlet

Can exceed MSSM bound


EE66SSM Higgs hSSM Higgs h11 mass mass boundbound

2

2 22 2 2 2 2 21 14 4sin 2 cos 2 1 cos 2 160

2h Z Zm v M M GeV

ESSM

NMSSM

MSSM

SFK,Moretti,Nevzorov

2-loop Higgs mass bounds

Observing a heavy Higgs boson @ LHC is one way (only way!) to distinguish the E6SSM from the NMSSM or MSSM Higgs sectors


Z’ Phenomenology in Z’ Phenomenology in EE66SSMSSM

'1 ZM g S



Exotic D-quarks in EExotic D-quarks in E66SSM @ SSM @ LHCLHC

300Dm GeV

Inv. mass distribution


Total cross section


Non-Higgsino discovery difficult Non-Higgsino discovery difficult due to small cross-section @ LHCdue to small cross-section @ LHC


Some ESome E66SSM Challenges SSM Challenges for the LHC Inverse for the LHC Inverse

Problem Problem Discover:

• the Z’, SUSY, the Higgs, the exotic D-quarks, the non-Higginos (Pythia needs to be extended -- Brent Nelson)

Measure:

• the Z’ mass and width and show that it is from U(1)N of the E6SSM with g’¼ g1

• the lightest Higgs boson mass and see if it exceeds the NMSSM limit

• the SUSY and exotic fermion spectrum

Deduce:

• the exotic couplings and SUSY soft masses at low energy

• the SUSY masses at the GUT scale


E6 MGUT

TeV

MString E8 £ E8 ! E

6

Superpartners, Z’, Exotics 5+5-bar’s

RH s

MW

Running Running upup

MR3

MR2

MR1

gaugino masses


Final remarksFinal remarks

Running up the soft scalar masses will be tricky due to:

•Large exotic fermion masses which must be disentangled

•Exotic thresholds in the TeV region

•Extra U(1)N leading to additional D-term contribution to soft masses (see next talk by David Morrissey)

Such issues are presently under discussion at this workshop (with Gordy Kane, Lisa Everett,..)

reproducing an e 6 ssm from its signatures

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